For the function f(x, y) - y? find a unit tangent vector to the level curve at the point 3 (- 4, 5) that has a positive x component. Hint: Think about how the tangent to the level curve relates to the gradient vector.

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x3 − y3,…

A: The gradient of the function f(x,y) is given by, ∇f(x,y)=∂f∂xi+∂f∂yj So,…

Q: Find the equation of the tangent plane to z=e^y+x+x^5+10   at the point (3,0,257)

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Q: If the gradient of f is ∇f=y3j−xi+zyk and the point P=(−8,6,2) lies on the level surface f(x,y,z)=0,…

A: To find the equation

Q: Find the gradient of the function at the given point. g(x, y) 11xe/x (13, 0) %3D Vg(13, 0) =

A: Gradient

Q: Find the gradient of the function g(x,y) = xy at the point (3, - 1). Then sketch the gradient…

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Q: 03. The equation of the tangent plane to the surface f(x, y) at the point (1,1) is 2x + 2y = 9,…

A: the surface is fx,y the gradient to the surface at (1,1) is ∇fx,y Let the value of the gradient is…

Q: Use the gradient to find the directional derivative of the function at P in the direction of v. w =…

A: w=y2+xz,   P1, 4, 4,  v=2i-j+2k Now the gradient is, ∇wx, y, z=wxx, y, z, wyx, y, z, wzx, y, z=z,…

Q: Find an equation of the tangent plane at the given point. f (x, y) = x^2y + xy^3,  (2, 1)

A: To Find an equation of the tangent plane at the given point. f (x, y) = x^2y + xy^3,  (2, 1)

Q: Find an equation for the tangent plane to the function f (x, y) = Jy – x at (1,2,1). %3D

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Q: Find the equation of the tangent plane to z=e^y+x+x^2+10 at the point (2,0,17).

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Q: Find the rightward-pointing (positive x-direction) unit tangent to the curve P = {(x, y) E R² |y =…

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Q: Find the equation of the tangent plane to z = e* + y + y° +1 at the point (0, 4, 70).

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Q: Let f(x, y) = 2xy – 4x² + 3y². %3D Then a standard equation for the tangent plane to the graph of f…

A: The function is given. Find the partial derivative fx and fy at the given point. Given,…

Q: Use the gradient to find the directional derivative of the function at P in the direction of v. h(x,…

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Q: Find the equation of the tangent plane to z=e^y+x+x^4+6 at the point (4,0,267).

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Q: Find the equation of the tangent plane to z=e^x+y+y^2+ 9 at the point (0,4,30)

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Q: Suppose we know that for a function f we have Vf(x, y) = (6x, 6). Find the directional derivative of…

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Q: 25 Find the gradient of f(x, y) : at (-2, 1). x² + y? NOTE: Enter the exact answer. grad f =|? i+ ?…

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Q: Find the equation of the tangent plane to z = e® +y+y +1 at the point (0, 2, 12). 2 =

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Q: Use the gradient to find the directional derivative of the function at P in the direction of Q. f(x,…

A: We know that the directional derivative of a function f(x, y) at a point P in the direction of a…

Q: b) Find the gradient of the tangent to the curve y= at the point with x=1.

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Q: Find the directional derivative of f at the given point in the direction indicated by the angle 0.…

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Q: If the gradient of f is Vf = r'j- 3yi+ 2zz k and the point P = (-4,-4, 1) lies on the level surface…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x3 – y3, P(6,…

A: Solution is given below:

Q: (a) Find the gradient of the curve at the point Q. (b) Given that the product of gradients of…

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Q: Find an equation for the tangent plane of z 3.xy? + y + 2 at the point (-1, 1, 0).

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Q: If the gradient of f is Vf = yj – z i+ 2xy k and the point P = (-3, 7, 8) lies on the level surface…

A: We have to find an equation for the tangent plane to the surface at the point P(-3, 7,8).

Q: If f(x, y) = xy, find the gradient vector Vf(7, 5) and use it to find the tangent line to the level…

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Q: Let f (x,y)=x2+5xy−4y2. Then a standard equation for the tangent plane to the graph of f at the…

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Q: Find the directional derivative of f at the given point in the direction indicated by the angle 0.…

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Q: u(x, y) = arctan a = (-1,0)

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Q: For the function z = f(x, y) = x² − xy² + y³, find the equations of the tangent lines in both the…

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Q: Find the directional derivative of the function f(z, v) = /1+ z*y? 32 (1+ x*y? at the point (1, 1)…

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Q: Find the equation of the tangent plane to z = e" + x + x² + 6 at the point (5, 0, 37).

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Q: If the gradient of f is Vf = x? j – z i+ 3yx k and the point P = (-4, 3, 1) lies on the level…

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Q: The gradient of the tangent to the curve y = 2e"- 3e" at the point where x=0 is %3D A 5. B 7. C -L D…

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Q: Given function f(x, y) = xy² - x² + 5y. a) Find the maximum rate of change of f at the point (1, -2)…

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Q: Determine the gradient and equation of the tangent to the curve f(x, y) = 0 in the point or (a)…

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Q: Find the gradient of f(r, h) = 2ärh + ár² at (6,3). NOTE: Enter the exact answer.

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Q: Find the gradient vector of the given function at the given point p. Then find the equation of the…

A: The given function is Fx,y=x3y+3xy2, p=2,-2 The main objective is to find the gradient vector and…

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

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Q: If the gradient of f is Vf = x³ } – zỉ+ 2yx k and the point P = ( surface f (x, y, z) = 0, find an…

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Q: Find the equation of the tangent plane to f(x,y)=√2xy+ 1 at the point            (2, 2),and use it…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x3 - y3, P(4,…

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Q: Consider the paraboloid f(x.y) = 9--r and the point P(12,0) on the level curve f(x.y) = 0. Compute…

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Q: Find the directional derivative of the function at P in the direction of v. V2 f(x, y) = x3 - y3,…

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Q: For the function f(x,y)=(4−x^2−y^2)/−5, find a unit tangent vector to the level curve at the point…

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Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

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Q: Use the gradient to find the directional derivative of the function at P in the direction of v. h(x,…

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